Safety, Tolerability, Pharmacokinetics, and Biological Activity of ATYR1940 in Adult Participants With Muscular Dystrophy

Inclusion Criteria: * Participant is a male or female aged 18 to 65 years, inclusive. * Participant has an established, genetically-confirmed, diagnosis of FSHD with clinical findings meeting existing criteria. * Participant has provided written informed consent after the nature of the study has been explained and prior to the performance of any research-related procedures. * Participant is, in the Investigator's opinion, willing and able to comply with all study procedures. * Cohorts ≥2 only: Participant has imaging findings meeting defined criteria for muscle inflammation in at least 1 skeletal muscle. Exclusion Criteria: * Participant is currently receiving treatment with an immunomodulatory agent or has a history of such treatment, including targeted biological therapies (for example, etanercept, omalizumab) within the 3 months before Baseline; corticosteroids within 4 weeks before Baseline; or high-dose non-steroidal anti-inflammatory agents (NSAIDs) within 2 weeks before Baseline. * Participant is currently receiving curcumin or albuterol or requires such treatment during study participation. * Participant has evidence of an alternative diagnosis other than FSHD, based on prior muscle biopsy or genetic test findings. * Participant has a presumptive diagnosis of FSHD, based on clinical assessment, but does not yet have genetic confirmation of the diagnosis. * Participant has a severe retinopathy. * Participant has a history of obstructive or restrictive lung disease (including interstitial lung disease, pulmonary fibrosis, or asthma), or evidence for interstitial lung disease on Screening chest radiograph. * Participant has a history of anti-synthetase syndrome, prior Jo-1 antibody (Ab)-positivity, or has a positive or equivocally positive Jo-1 Ab test result during Screening. * Participant has acute or clinically relevant Epstein-Barr virus or cytomegalovirus infection or re-activation. * Participant has a chronic infection such as hepatitis B virus, hepatitis C virus, or human immunodeficiency virus or a history of tuberculosis. * Participant has received a vaccination within 8 weeks before Baseline or vaccination is planned during study participation. * Participant has symptomatic cardiomyopathy or severe cardiac arrhythmia that may, in the Investigator's opinion, limit the participant's ability to complete the study protocol. * Participant has anemia (as defined for participant's age and gender by local laboratory range). * Participant has gamma-glutamyl transferase (GGT) or serum creatinine levels \>2 × the upper limit of normal (ULN). * Participant has abnormal baseline findings, medical condition(s), or laboratory findings that, in the Investigator's opinion, might jeopardize participant's safety or decrease the chance of obtaining satisfactory data needed to achieve the objectives of the study. * Participant has evidence of clinically significant cardiovascular, pulmonary, hepatic, renal, hematological, metabolic, dermatological, or gastrointestinal disease, or has a condition that requires immediate surgical intervention or other treatment or may not allow safe participation. * Participant has used any investigational product or device (other than a mobility assistance device) within 30 days before Baseline. * Participant has received a product intended to enhance muscle growth within 30 days before Baseline. * Participant underwent muscle biopsy within 30 days before Baseline. * Participant initiated treatment with a statin or had a significant adjustment to their statin regimen within 3 months before Baseline. (Stable, chronic statin use is permissible.) * Participant has received a product that putatively enhances muscle growth (for example, insulin-like growth factor, growth hormone) or activity (for example, Coenzyme A) on a chronic basis within 4 weeks before Baseline. * Participant is unwilling to abstain from strenuous physical activity for 24 hours prior to each study center visit. * Participant previously received ATYR1940. * If female and of childbearing potential (premenopausal and not surgically sterile), participant has a positive pregnancy test at Screening or is unwilling to use contraception from the time of Screening through 1 month after the last Study Drug dose. Acceptable methods of birth control include abstinence, barrier methods, hormones, or intra-uterine device. * If male, participant is unwilling to use a condom plus spermicide during sexual intercourse from the time of Screening through 1 month after the last Study Drug dose. * Cohorts ≥2 only: Participant has a known contraindication for magnetic resonance imaging (MRI) assessments (for example metal prosthesis or pacemaker) as per local site MRI protocol